If the area of a square A has area 24 cm2, then what is the area of another square B having diagonal two-third of the diagonal of A?
If the area of a square A has area 24 cm2, then what is the area of another square B having diagonal two-third of the diagonal of A?
1). 26 cm2
2). 42.5cm2
3). 32/3 cm2
4). 38.6 cm2
1 answers
Solution:
Given: Area of square A = 24 sq.cm
To find : Area of square B = ?
Let us take the side of square A as 'a' and square B as 'b'.
So, a²= 24 sq.cm
a = √24
a = 2√6 cm.
It is given that,
Diagonal of square B = two-third of the diagonal of square A
We know that diagonal of a square = √2 of side of a square
So, √2 (b) = (⅔)√2 (a)
b = (⅔) a
Substituting the value of a in here we have
b = ⅔ ( 2√6 )
b = ( 2 × 2√2 √3 ) / (√3 √3)
b = (4 √2)/√3 cm
Area of square B = b² cm²
Area of square B =[(4 √2)/√3]² cm²
Area of square B = (16×2) / 3 cm²
Area of square B = 32/3 cm²
So,the correct option is 3). 32/3 cm²